Are there any labs out there that would process and store cord blood units? for a fee. We are looking to partner with someone who could do this while we establish our business locally.

This is a very old topic, but in case anyone else needs the answer: with the current advances in technology a quick internet search lists several companies that now commercially store cord blood samples.

https://duckduckgo.com/?t=ffab&q=cord+blood+storage&ia=web

From a clinical laboratory standpoint, no lab I have worked in has had the space to store cord units for a business being established.  In addition, cord units are generally frozen and stored in liquid nitrogen, and most clinical labs do not use this storage method at all, or in bulk.

Quick search - ViaCord